On the structure and diversity of rational beliefs

by Mordecai Kurz

ECONOMIC THEORY Volume 4, Number 6 (1994), 877-900.

Abstract

The paper proposes that the theory of expectations be reformulated under the assumption that agents do not know the structural relations (such as equilibrium prices) of the economy. Instead, we postulate that they can observe past data of the economy and form probability beliefs based on the data generated by the economy. Using past data agents can compute relative frequencies and the basic assumption of the theory is that the system which generates the data is stable in the sense that the empirically computed relative frequencies converge. It is then shown that the limit of these relative frequencies induce a probability on the space of infinite sequences of the observables in the economy. This probability is stationary. Abelief of an agent is a probability on the space of infinite sequences of the observable variables in the economy. Such a probability represents the "theory" or "hypothesis" of the agent about the mechanism which generates the data. A belief is said to becompatible with the data if under the proposed probability belief the economy would generate the same limit of the relative frequencies as computed from the real data. A theory which is compatible with the data is a theory which cannot be rejected by the data. A belief is said to be aRational Belief if it is (i) compatible with the data and (ii) satisfies a certain technical condition. The Main Theorem provides a characterization of all Rational Beliefs.